In retail, there are predictable yet dramatic time-dependent patterns in customer behavior, such as periodic changes in the number of visitors, or increases in visitors just before major holidays. The current paradigm of multi-armed bandit analysis does not take these known patterns into account. This means that for applications in retail, where prices are fixed for periods of time, current bandit algorithms will not suffice. This work provides a remedy that takes the time-dependent patterns into account, and we show how this remedy is implemented in the UCB and {\epsilon}-greedy methods and we introduce a new policy called the variable arm pool method. In the corrected methods, exploitation (greed) is regulated over time, so that more exploitation occurs during higher reward periods, and more exploration occurs in periods of low reward. In order to understand why regret is reduced with the corrected methods, we present a set of bounds that provide insight into why we would want to exploit during periods of high reward, and discuss the impact on regret. Our proposed methods perform well in experiments, and were inspired by a high-scoring entry in the Exploration and Exploitation 3 contest using data from Yahoo! Front Page. That entry heavily used time-series methods to regulate greed over time, which was substantially more effective than other contextual bandit methods.

This paper examines the speaker identification potential of breath sounds in continuous speech. Speech is largely produced during exhalation. In order to replenish air in the lungs, speakers must periodically inhale. When inhalation occurs in the midst of continuous speech, it is generally through the mouth. Intra-speech breathing behavior has been the subject of much study, including the patterns, cadence, and variations in energy levels. However, an often ignored characteristic is the {\em sound} produced during the inhalation phase of this cycle. Intra-speech inhalation is rapid and energetic, performed with open mouth and glottis, effectively exposing the entire vocal tract to enable maximum intake of air. This results in vocal tract resonances evoked by turbulence that are characteristic of the speaker's speech-producing apparatus. Consequently, the sounds of inhalation are expected to carry information about the speaker's identity. Moreover, unlike other spoken sounds which are subject to active control, inhalation sounds are generally more natural and less affected by voluntary influences. The goal of this paper is to demonstrate that breath sounds are indeed bio-signatures that can be used to identify speakers. We show that these sounds by themselves can yield remarkably accurate speaker recognition with appropriate feature representations and classification frameworks.

Both the human brain and artificial learning agents operating in real-world or comparably complex environments are faced with the challenge of online model selection. In principle this challenge can be overcome: hierarchical Bayesian inference provides a principled method for model selection and it converges on the same posterior for both off-line (i.e. batch) and online learning. However, maintaining a parameter posterior for each model in parallel has in general an even higher memory cost than storing the entire data set and is consequently clearly unfeasible. Alternatively, maintaining only a limited set of models in memory could limit memory requirements. However, sufficient statistics for one model will usually be insufficient for fitting a different kind of model, meaning that the agent loses information with each model change. We propose that episodic memory can circumvent the challenge of limited memory-capacity online model selection by retaining a selected subset of data points. We design a method to compute the quantities necessary for model selection even when the data is discarded and only statistics of one (or few) learnt models are available. We demonstrate on a simple model that a limited-sized episodic memory buffer, when the content is optimised to retain data with statistics not matching the current representation, can resolve the fundamental challenge of online model selection.

We introduce a framework to study the effective objectives at different time scales of financial market microstructure. The financial market can be regarded as a complex adaptive system, where purposeful agents collectively and simultaneously create and perceive their environment as they interact with it. It has been suggested that multiple agent classes operate in this system, with a non-trivial hierarchy of top-down and bottom-up causation classes with different effective models governing each level. We conjecture that agent classes may in fact operate at different time scales and thus act differently in response to the same perceived market state. Given scale-specific temporal state trajectories and action sequences estimated from aggregate market behaviour, we use Inverse Reinforcement Learning to compute the effective reward function for the aggregate agent class at each scale, allowing us to assess the relative attractiveness of feature vectors across different scales. Differences in reward functions for feature vectors may indicate different objectives of market participants, which could assist in finding the scale boundary for agent classes. This has implications for learning algorithms operating in this domain.

One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGLD is a standard stochastic gradient descent to which is added a controlled amount of noise, specifically scaled so that the parameter converges in law to the posterior distribution [WT11, TTV16]. The posterior predictive distribution can be approximated by an ensemble of samples from the trajectory. Choice of the variance of the noise is known to impact the practical behavior of SGLD: for instance, noise should be smaller for sensitive parameter directions. Theoretically, it has been suggested to use the inverse Fisher information matrix of the model as the variance of the noise, since it is also the variance of the Bayesian posterior [PT13, AKW12, GC11]. But the Fisher matrix is costly to compute for large- dimensional models. Here we use the easily computed Fisher matrix approximations for deep neural networks from [MO16, Oll15]. The resulting natural Langevin dynamics combines the advantages of Amari's natural gradient descent and Fisher-preconditioned Langevin dynamics for large neural networks. Small-scale experiments on MNIST show that Fisher matrix preconditioning brings SGLD close to dropout as a regularizing technique.

Many computationally-efficient methods for Bayesian deep learning rely on continuous optimization algorithms, but the implementation of these methods requires significant changes to existing code-bases. In this paper, we propose Vprop, a method for Gaussian variational inference that can be implemented with two minor changes to the off-the-shelf RMSprop optimizer. Vprop also reduces the memory requirements of Black-Box Variational Inference by half. We derive Vprop using the conjugate-computation variational inference method, and establish its connections to Newton's method, natural-gradient methods, and extended Kalman filters. Overall, this paper presents Vprop as a principled, computationally-efficient, and easy-to-implement method for Bayesian deep learning.

This paper proposes a new algorithm for controlling classification results by generating a small additive perturbation without changing the classifier network. Our work is inspired by existing works generating adversarial perturbation that worsens classification performance. In contrast to the existing methods, our work aims to generate perturbations that can enhance overall classification performance. To solve this performance enhancement problem, we newly propose a perturbation generation network (PGN) influenced by the adversarial learning strategy. In our problem, the information in a large external dataset is summarized by a small additive perturbation, which helps to improve the performance of the classifier trained with the target dataset. In addition to this performance enhancement problem, we show that the proposed PGN can be adopted to solve the classical adversarial problem without utilizing the information on the target classifier. The mentioned characteristics of our method are verified through extensive experiments on publicly available visual datasets.

The problem of universal outlying sequence detection is studied, where the goal is to detect outlying sequences among $M$ sequences of samples. A sequence is considered as outlying if the observations therein are generated by a distribution different from those generating the observations in the majority of the sequences. In the universal setting, we are interested in identifying all the outlying sequences without knowing the underlying generating distributions. In this paper, a class of tests based on distribution clustering is proposed. These tests are shown to be exponentially consistent with linear time complexity in $M$. Numerical results demonstrate that our clustering-based tests achieve similar performance to existing tests, while being considerably more computationally efficient.

We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the conditional gradient method. Unlike many existing approaches, our algorithm solves the original infinite-dimensional (for splines of degree at least two) optimization problem without pre-specified knot locations. We then adapt our algorithm to fit generalized additive models with saturating splines as coordinate functions and show that the saturation requirement allows our model to simultaneously perform feature selection and nonlinear function fitting. Finally, we briefly sketch how the method can be extended to higher order splines and to different requirements on the extension outside the data range.

We propose a practical method for $L_0$ norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of $L_0$ regularization. However, since the $L_0$ norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected $L_0$ norm of the resulting gated weights is differentiable with respect to the distribution parameters. We further propose the \emph{hard concrete} distribution for the gates, which is obtained by "stretching" a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer.